Converting you Mini-DV to DVDs
This is fairly straightforward, actually. And while you have mini-DV, it really wouldn't matter what format of camcorder you had as long as we were talking about a digital camcorder (coming from an analog camcorder is different and requires some different hardware).
Most digital camcorders have a Firewire (sometimes known as IEEE 1394) interface. Most modern computers, especially laptops, also have a Firewire interface. If not, your first task is to get a Firewire interface for the target computer. If necessary, this is an independent task that is not directly related to the video task. You may also need to get a suitable cable (4-pin, 6-pin or possibly 6-pin on one end to 4-pin on the other).
[Some camcorders will have USB interfaces instead of or in addition to a Firewire interface. If so, fine, but in many cases the image quality from the USB interface (if there is one) will be inferior to that from the Firewire interface.]
You will probably next need to install Windows drivers for your camcorder on your PC, so that the camcorder will be recognized by the PC when they are connected. The drivers should have come with the Camcorder, or should be available on the web site of the camcorder manufacturer.
Finally, you will need to install some video editing software that can capture the video from the camcorder and also allow you do some editing. To some extent, this depends on the video format that comes out of the camcorder ... it may be Uncompressed AVI (actually the best format for editing in SOME ways, but the files are HUGE (more than 10 GIGABYTES per hour), it may be MPEG or it may be MPEG2. In a few cases, it may be yet something else. The video software has to be able to deal with the file format that is output by the camcorder. It's likely that most video software will work with most camcorders, but it's something to be aware of as in some cases it may limit your choice of software. Again, it's very possible that such software came with the camcorder. You can also use Microsoft Windows Movie Maker, or you can buy a product like Pinacle Studio that has this capability. Another thing to note for the burning step (below) is that the full retail versions of the two major CD & DVD burning programs (Roxio (now Sonic) Easy Media Creator and Nero) both have all the software that you will need in most cases, but in neither case is their editing software necessarily the best available.
Whatever software you select, this software will need to let you get the video from the camcorder and save it on the PC as a file (the file size will be large, gigabytes per hour probably and in some cases tens of giabytes per hour). That completes the first step.
The next step is to edit the video into your desired content. This is entirely a function of the video editing software that you use. Simple software (Windows Movie Maker) can do cut and paste; more complex software can do eleaborate video production with multiple video streams being merged, often with "chroma key" (blue or green screen used to put part of one video stream (often a person) "into" another video stream). There are a lot of choices here, with a wide range of cost and a wide range of ease of use.
Finally, you need to do DVD authoring, which is where you will (if you want to) create "menus" and "chapters" for putting the video onto a DVD. Some of the major editing software packages (Pinacle) have both the video editing and the DVD authoring functions built-in, while in other cases you will use one program for video editing, and another program for DVD authoring. For example, Windows Movie Maker, which has reasonable cut-and-paste video editing, does not, by itself, have the DVD authoring capability. But Pinacle, and the Roxio and Nero products, do have both editing and DVD authoring. The final step of DVD authoring will actually write the DVD from the video. Note that if the video has to be re-encoded into MPEG2 (very likely) this step can take a LONG time (hours; on some computers, more than 12 hours for a one- or two-hour video).
I hope that gives you an overview of the process and what is involved. Look for some user reviews of the available software packages. In general, there is a very large trade-off between capabilities and ease-of-use, but most people are only looking for simple "cut-and-paste" editing and not for the capabilities that would in used by commercial video production applications.
By the way, do NOT use DVD-RW media. I don't recommend RW media (either CD or DVD) for ANYTHING. It is not a good archival media and precisely because such media is not "permanent", sometimes data written to such media "fades" over time (I will accept both that it should not happen, and that if it does, it's because the hardware was defective ... that doesn't matter ... it DOES happen, too often). On top of the RW media is slow to burn and expensive. With CD media at about a penny per disc and DVD media at about 20 cents per disc, just use one-time media, and if you want to redo the project, use a new media. It's cheap enough that the cost just shouldn't be an issue, and it's faster (a lot faster), cheaper and more reliable and permanent than RW media.